Running principal component and k-means clustering analyses

dir.create("./results", showWarnings = F)
dir.create("./results/figures", showWarnings = F)
source("./src/GM_stats.R")

Performing GPA

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Making projections... Finished!

[1] -0.9999859
[1] 0.9999956
[1] -0.9999535
[1] -0.9999967
[1] -0.999442
[1] -0.9999388
[1] -1
[1] 0.9997545
[1] -0.9996835
[1] 0.9999969

Plotting PC and k-means results

K-means clustering plot:

Kennel-club groupings and PC results:

Too few points to calculate an ellipse

Discriminant Factors between groups

Comparison of landmarks between group means

# Extracting first 5 PCs and each kennel-club grouping scheme
skulls <- cbind(SlicerMorph.repc[, 1:5], 
                "UKC" = factor(SlicerMorph.repc$UKC, ordered = T, levels = UKC_group_order), 
                "AKC" = factor(SlicerMorph.repc$AKC, ordered = T, levels = AKC_group_order),
                "bitework" = factor(SlicerMorph.repc$Bitework),
                "scentwork" = factor(SlicerMorph.repc$Nosework))
skulls <- na.omit(skulls)

# Create a paired and ordered GPA-grouping object
mixdrop<-gpa$coords[,,order(dimnames(gpa$coords)[[3]])]
mixdrop<-mixdrop[,,-96]

reforge<-geomorph.data.frame(shape = mixdrop,
                             UKC = na.omit(factor(SlicerMorph.repc$UKC, ordered = T)),
                             AKC = na.omit(factor(SlicerMorph.repc$AKC, ordered = T)),
                             bitework = na.omit(factor(SlicerMorph.repc$Bitework[-96])),
                             scentwork = na.omit(factor(SlicerMorph.repc$Nosework[-96])))

# Create a function that subsets the mean landmarks for each group and does a pairwise subtraction and squaring of those means
meanforge <- function(target, group) {
  #sub-setting the means and sending them to a new object
  new.coords<-coords.subset(target[["shape"]], group = target[[group]])
  output_means<-lapply(new.coords, mshape)
  #perform the subtraction and squaring of the pairwise combinations
  result<- combn(output_means, 2, function(x) (x[[1]]-x[[2]])^2, simplify = FALSE)
  #rename the pairs so they're readable
  names(result)<-combn(names(output_means), 2, function(n) paste(n[1], "-", n[2]), simplify = TRUE)
  return(result)
}

#now run the function for each grouping scheme. Each member of the list will be named based on which two groups are compared
meanshape.UKC<-meanforge(reforge,"UKC")
meanshape.AKC<-meanforge(reforge,"AKC")
meanshape.nose<-meanforge(reforge,"scentwork")
meanshape.bite<-meanforge(reforge,"bitework")

Reformatting data for visualization:

calc_gpa_dist <- function(dat){
  require(tidyr)
  n <- length(names(dat))
  results <- matrix(NA, nrow = nrow(dat[[1]]), ncol = n)
  results <- as.data.frame(results)
  results <- cbind(seq(1,nrow(results)), results)
  colnames(results) <- c("landmark",names(dat))
  
  for(i in names(dat)){
    results[[i]] <- sqrt(dat[[i]][,"X"]^2 + dat[[i]][,"Y"]^2 + dat[[i]][,"Z"]^2)
  }
  results_long <- pivot_longer(results, cols = -"landmark", names_to = "comparison")
  results_long$landmark <- factor(results_long$landmark)
  return(results_long)
}

meanshape.AKC[["plotting"]] <- calc_gpa_dist(meanshape.AKC)
meanshape.UKC[["plotting"]] <- calc_gpa_dist(meanshape.UKC)
meanshape.bite[["plotting"]] <- calc_gpa_dist(meanshape.bite)
meanshape.nose[["plotting"]] <- calc_gpa_dist(meanshape.nose)

meanshape.AKC[["plotting"]]$short <- ifelse(grepl("toy", meanshape.AKC[["plotting"]]$comparison, 
                                                  ignore.case = T),
                                           "toy", 
                                           ifelse(grepl("natural", meanshape.AKC[["plotting"]]$comparison,
                                                        ignore.case = T),
                                                  "natural", "other"))
meanshape.AKC[["plotting"]]$short <- factor(meanshape.AKC[["plotting"]]$short, 
                                            ordered = T, levels = c("toy", "natural", "other"))
meanshape.UKC[["plotting"]]$short <- ifelse(grepl("companion", meanshape.UKC[["plotting"]]$comparison,
                                                      ignore.case = T),
                                           "companion", 
                                           ifelse(grepl("natural", meanshape.UKC[["plotting"]]$comparison,
                                                      ignore.case = T),
                                           "natural", "other"))
meanshape.UKC[["plotting"]]$short <- factor(meanshape.UKC[["plotting"]]$short, 
                                            ordered = T, levels = c("companion", "natural", "other"))

AKC & UKC groups:

p_UKC_compare <- ggplot(meanshape.UKC[["plotting"]], aes(landmark, value, color = short)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.UKC[["cutoff"]]$mean+2*meanshape.UKC[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Comparison against") +
  ylab("DFA distance squared") +
  ggtitle("UKC group comparisons") +
  theme_bw() + 
  theme(legend.position = "inside", legend.position.inside = c(0.75,0.65),
        legend.background = element_rect(color = "gray30", fill = "white", linetype="solid",
                                         linewidth = 0.2))

p_AKC_compare <- ggplot(meanshape.AKC[["plotting"]], aes(landmark, value, color = short)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.AKC[["cutoff"]]$mean+2*meanshape.AKC[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Comparison against") +
  ylab("DFA distance squared") +
  ggtitle("AKC group comparisons") +
  theme_bw() +
    theme(legend.position = "inside", legend.position.inside = c(0.75,0.65),
        legend.background = element_rect(color = "gray30", fill = "white", linetype="solid",
                                         linewidth = 0.2))
p_AKC_compare / p_UKC_compare

Nosework and Bitework:

p_bite_compare <-  ggplot(meanshape.bite[["plotting"]], aes(landmark, value, color = comparison)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.bite[["cutoff"]]$mean+2*meanshape.bite[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Group-group\ncomparison") +
  ylab("DFA distance squared") +
  ggtitle("Bite-work group comparisons") +
  theme_bw()
p_nose_compare <- ggplot(meanshape.nose[["plotting"]], aes(landmark, value, color = comparison)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.nose[["cutoff"]]$mean+2*meanshape.nose[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Group-group\ncomparison") +
  ylab("DFA distance squared") +
  ggtitle("Scent-work group comparisons") +
  theme_bw()

p_bite_compare / p_nose_compare + plot_layout(guides = "collect")

MANOVA

man_UKC <- manova(as.matrix(skulls[,1:5])~skulls$UKC)
summary.aov(man_UKC, test="Pillai")
 Response PC.1 :
             Df  Sum Sq  Mean Sq F value    Pr(>F)    
skulls$UKC    8 0.65020 0.081275  35.372 < 2.2e-16 ***
Residuals   107 0.24585 0.002298                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 Response PC.2 :
             Df   Sum Sq   Mean Sq F value    Pr(>F)    
skulls$UKC    8 0.073427 0.0091783  6.0866 1.902e-06 ***
Residuals   107 0.161352 0.0015080                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 Response PC.3 :
             Df   Sum Sq    Mean Sq F value  Pr(>F)  
skulls$UKC    8 0.016265 0.00203313  2.4906 0.01612 *
Residuals   107 0.087348 0.00081633                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 Response PC.4 :
             Df   Sum Sq    Mean Sq F value    Pr(>F)    
skulls$UKC    8 0.024974 0.00312178  5.7231 4.625e-06 ***
Residuals   107 0.058365 0.00054547                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 Response PC.5 :
             Df   Sum Sq    Mean Sq F value Pr(>F)
skulls$UKC    8 0.000574 0.00007179  0.1633 0.9951
Residuals   107 0.047029 0.00043952               
lda_UKC <- MASS::lda(skulls$UKC~as.matrix(skulls[,1:5]))
lda_UKC
Call:
lda(skulls$UKC ~ as.matrix(skulls[, 1:5]))

Prior probabilities of groups:
       NATURAL        Herding        Terrier      Companion        Gun dog       Guardian 
    0.19827586     0.23275862     0.08620690     0.12068966     0.05172414     0.09482759 
Northern Breed     Sighthound     Scenthound 
    0.02586207     0.14655172     0.04310345 

Group means:
               as.matrix(skulls[, 1:5])PC.1 as.matrix(skulls[, 1:5])PC.2 as.matrix(skulls[, 1:5])PC.3
NATURAL                         -0.11869015                 -0.019063433                   0.04817564
Herding                         -0.12101159                  0.026436494                   0.04577986
Terrier                         -0.05852371                  0.001880539                   0.04485686
Companion                        0.09983210                  0.018101105                   0.02331451
Gun dog                         -0.11168214                  0.041234328                   0.04624008
Guardian                        -0.06180271                  0.065382213                   0.06595086
Northern Breed                  -0.06497801                  0.049661060                   0.06220728
Sighthound                      -0.15480497                  0.029842740                   0.02964807
Scenthound                      -0.12915491                  0.049368307                   0.04321946
               as.matrix(skulls[, 1:5])PC.4 as.matrix(skulls[, 1:5])PC.5
NATURAL                        -0.016530397                    0.1158473
Herding                         0.013615782                    0.1190599
Terrier                         0.032376419                    0.1152870
Companion                       0.011348484                    0.1182048
Gun dog                         0.007520818                    0.1204955
Guardian                        0.003014570                    0.1207284
Northern Breed                 -0.017512289                    0.1170088
Sighthound                      0.018704155                    0.1147247
Scenthound                      0.010813419                    0.1131374

Coefficients of linear discriminants:
                                    LD1        LD2        LD3       LD4          LD5
as.matrix(skulls[, 1:5])PC.1  21.465233   2.072852   2.157478  1.232714   0.61490553
as.matrix(skulls[, 1:5])PC.2   2.130815 -20.151953  14.104686 -8.508683   1.48405135
as.matrix(skulls[, 1:5])PC.3 -13.131521   1.216403  21.217452 26.189753   4.17032936
as.matrix(skulls[, 1:5])PC.4  10.561161 -31.562092 -23.132983 17.258716  -0.02015756
as.matrix(skulls[, 1:5])PC.5   2.636558  -2.368104   6.558913  4.347214 -46.98480500

Proportion of trace:
   LD1    LD2    LD3    LD4    LD5 
0.7331 0.1664 0.0818 0.0172 0.0015 

Testing of Functional Groups

bite_yes_canine <- bite_data$canine[bite_data$Bitework == "yes"]
bite_no_canine <- bite_data$canine[bite_data$Bitework == "no"]
shapiro.test(bite_yes_canine)

    Shapiro-Wilk normality test

data:  bite_yes_canine
W = 0.95076, p-value = 0.5726
shapiro.test(bite_no_canine)

    Shapiro-Wilk normality test

data:  bite_no_canine
W = 0.97244, p-value = 0.08128
t.test(bite_yes_canine, bite_no_canine)

    Welch Two Sample t-test

data:  bite_yes_canine and bite_no_canine
t = -0.30306, df = 36.495, p-value = 0.7636
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -9.152725  6.771939
sample estimates:
mean of x mean of y 
 57.78286  58.97325 
bite_yes_carnassial <- bite_data$carnassial[bite_data$Bitework == "yes"]
bite_no_carnassial <- bite_data$carnassial[bite_data$Bitework == "no"]
shapiro.test(bite_yes_carnassial)

    Shapiro-Wilk normality test

data:  bite_yes_carnassial
W = 0.92608, p-value = 0.2687
shapiro.test(bite_no_carnassial)

    Shapiro-Wilk normality test

data:  bite_no_carnassial
W = 0.96684, p-value = 0.03577
t.test(bite_yes_carnassial, bite_no_carnassial)

    Welch Two Sample t-test

data:  bite_yes_carnassial and bite_no_carnassial
t = -0.52911, df = 42.805, p-value = 0.5995
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -9.417946  5.503589
sample estimates:
mean of x mean of y 
 57.12857  59.08575 
bite_natural_canine <- bite_data$canine[bite_data$Bitework == "NATURAL"]
shapiro.test(bite_natural_canine)

    Shapiro-Wilk normality test

data:  bite_natural_canine
W = 0.91337, p-value = 0.2672
bite_fox_canine <- bite_data$canine[bite_data$Bitework == "FOX"]
shapiro.test(bite_fox_canine)

    Shapiro-Wilk normality test

data:  bite_fox_canine
W = 0.82835, p-value = 0.03197
t.test(bite_yes_canine, bite_natural_canine)

    Welch Two Sample t-test

data:  bite_yes_canine and bite_natural_canine
t = -1.6371, df = 13.462, p-value = 0.1248
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -29.241240   3.979681
sample estimates:
mean of x mean of y 
 57.78286  70.41364 
t.test(bite_yes_canine, bite_fox_canine)

    Welch Two Sample t-test

data:  bite_yes_canine and bite_fox_canine
t = -0.85342, df = 10.859, p-value = 0.4119
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -29.77613  13.15585
sample estimates:
mean of x mean of y 
 57.78286  66.09300 

For the paper:

Figure 2:

Too few points to calculate an ellipse

Too few points to calculate an ellipse

Figure 4:

Saving 10 x 7.5 in image
---
title: "Geomorphic Morphometrics on canid skulls"
output: html_notebook
---

```{r setup, include=FALSE, warning=FALSE, message=FALSE}
knitr::opts_knit$set(root.dir = rprojroot::find_rstudio_root_file())
knitr::opts_chunk$set(echo = TRUE, fig.width = 8.5)
options(knitr.graphics.error = FALSE)
options(knitr.kable.NA = '')
options(rgl.useNULL=TRUE) # Note: OpenGL is depreciated on Macs, and this will cause an error when loading the Morpho package. Setting this option removes the error. 

library(tidyverse)
library(janitor)
library(gtools)
library(ggplot2)
library(patchwork)
library(kableExtra)
library(ggrepel)
library(geomorph)
# devtools::install_github('SlicerMorph/SlicerMorphR')
library(SlicerMorphR)
# devtools::install_github("lindsaywaldrop/munchcolors")
library(munchcolors)
# devtools::install_github("zarquon42b/Morpho")
#library(Morpho)
```


## Running principal component and k-means clustering analyses

```{r}
dir.create("./results", showWarnings = F)
dir.create("./results/figures", showWarnings = F)
source("./src/GM_stats.R")
```

## Plotting PC and k-means results


```{r plotting-setup, include=FALSE}
# Setting UKC group order
UKC_group_order <- c("NATURAL", "Herding", "Terrier", "Companion", "Gun dog", 
                     "Guardian", "Northern Breed", "Sighthound", "Scenthound")
AKC_group_order <- c("NATURAL", "Herding", "Terrier", "Toy", "Sporting", 
                     "Working", "Non-sporting", "Hound")

# grouping plots ----------------------------------------------------------
# First added your ordered classifiers onto the PCA data
SlicerMorph.repc$UKC <- clsf_reord$UKC.breeding.Standard
SlicerMorph.repc$AKC <- clsf_reord$AKC.breeding.standard
# Set mixed breed to NA for plotting, there is only one!
SlicerMorph.repc$UKC[SlicerMorph.repc$UKC == "MIXED"] <- NA
SlicerMorph.repc$AKC[SlicerMorph.repc$AKC == "MIXED"] <- NA
# Setting fox to natural for AKC/UKC grouping to simplify plots
SlicerMorph.repc$UKC[SlicerMorph.repc$UKC == "FOX"] <- "NATURAL"
SlicerMorph.repc$AKC[SlicerMorph.repc$AKC == "FOX"] <- "NATURAL"

# Changing Yes to lowercase
SlicerMorph.repc$Nosework <- ifelse(clsf_reord$Nose =="Yes" | clsf_reord$Nose == "no", 
                                    tolower(clsf_reord$Nose), clsf_reord$Nose)
# Changing Nosework to ordered factor
SlicerMorph.repc$Nosework <- factor(SlicerMorph.repc$Nosework, ordered = T, 
                                    levels = c("yes", "no", "NATURAL", "FOX"))
# Changing Yes to lowercase 
SlicerMorph.repc$Bitework <- ifelse(clsf_reord$Bitework =="Yes" | clsf_reord$Bitework == "no",
                                    tolower(clsf_reord$Bitework), clsf_reord$Bitework)
# Changing Bitework to ordered factor
SlicerMorph.repc$Bitework <- factor(SlicerMorph.repc$Bitework, ordered = T, 
                                    levels = c("yes", "no", "NATURAL", "FOX"))
# Putting cluster levels into a column as a factor
SlicerMorph.repc$cluster <- factor(km$cluster)

# Now to ease viewing we'll factor them into broad categories

# Turning UKC isnto an ordered factor column
SlicerMorph.repc$UKC.shapefact <- factor(SlicerMorph.repc$UKC, ordered = T, 
                                         levels = UKC_group_order)

## AKC next
SlicerMorph.repc$AKC.shapefact <- factor(SlicerMorph.repc$AKC, 
                                         levels = AKC_group_order)

SlicerMorph.repc$AKC.fact <- factor(SlicerMorph.repc$AKC)

## Setting up a column that is domestic (dogs) and natural (foxes, others)
SlicerMorph.repc$domestic <- factor(ifelse(SlicerMorph.repc$UKC == "NATURAL" | 
                                             SlicerMorph.repc$UKC == "FOX", 
                                           "Natural", "Domesticated"), 
                                    ordered = T, levels = c("Domesticated", "Natural"))

```

K-means clustering plot: 

```{r k-means, echo=FALSE, warning=FALSE, fig.cap="K-means clustering plot."}
#now build the plot
pkmean <- ggplot(SlicerMorph.repc[!is.na(SlicerMorph.repc$UKC),], aes(PC.1, PC.2, color = cluster, 
                                   fill = cluster,
                                   shape = domestic)) + 
  geom_point(size = 2) +
  stat_ellipse(geom = "polygon", aes(fill = cluster, group = cluster), level = 0.95, alpha = 0.1) +
  scale_shape_manual(values = c(5, 19), name = " ") +
  scale_color_munch(choice = "Nietzsche", discrete = TRUE,name = "Cluster") + 
  scale_fill_munch(choice = "Nietzsche", discrete = TRUE, name = "Cluster") +
  geom_text_repel(label = SlicerMorph.repc$Breed[!is.na(SlicerMorph.repc$UKC)], max.overlaps = 4, show.legend = FALSE)+
  xlab("PC 1 (Var = 50.2%)") + ylab("PC 2 (Var = 13.3%)") +
  theme_bw()
pkmean
```

Kennel-club groupings and PC results:

```{r kc-groups, echo=FALSE, warning=FALSE, fig.cap="K-means clustering plot.", fig.height=5.5, fig.width=12}
#now build the plot
kc_palette <- munch_palette("Murderer", 8)
kc_palette <- c(kc_palette, kc_palette[2])
pUKC <- ggplot(SlicerMorph.repc[!is.na(SlicerMorph.repc$UKC),], aes(PC.1, PC.2, color = UKC.shapefact, 
                                   fill = UKC.shapefact,
                                   shape = UKC.shapefact)) + 
  geom_point(size = 2) +
  stat_ellipse(geom = "polygon", aes(group = UKC.shapefact), level = 0.95, alpha = 0.2) +
  scale_shape_manual(values = c(19, 0, 1, 2, 5, 6, 7, 9, 10), name = "UKC Groups") +
  scale_color_manual(values = kc_palette, name = "UKC Groups") + 
  scale_fill_manual(values = kc_palette, name = "UKC Groups") +
  geom_text_repel(label = SlicerMorph.repc$Breed[!is.na(SlicerMorph.repc$UKC)], max.overlaps = 4, show.legend = FALSE)+
  
  xlab("PC 1 (Var = 50.2%)") + ylab("PC 2 (Var = 13.3%)") +
  theme_bw()
pAKC <- ggplot(SlicerMorph.repc[!is.na(SlicerMorph.repc$AKC),], aes(PC.1, PC.2, color = AKC.shapefact, 
                                   fill = AKC.shapefact,
                                   shape = AKC.shapefact)) + 
  geom_point(size = 2) +
  stat_ellipse(geom = "polygon", aes(fill = AKC.shapefact, 
                                     group = AKC.shapefact), level = 0.95, alpha = 0.2) +
  scale_shape_manual(values = c(19, 0, 1, 2, 5, 6, 7, 9, 10), name = "AKC Groups") +
  scale_color_munch(choice = "Murderer", discrete = TRUE, name = "AKC Groups") + 
  scale_fill_munch(choice = "Murderer", discrete = TRUE, name = "AKC Groups") +
  geom_text_repel(label = SlicerMorph.repc$Breed[!is.na(SlicerMorph.repc$AKC)], max.overlaps = 4, show.legend = FALSE)+
  
  xlab("PC 1 (Var = 50.2%)") + ylab("PC 2 (Var = 13.3%)") +
  theme_bw()

pUKC + pAKC
```


## Discriminant Factors between groups

Comparison of landmarks between group means

```{r}
# Extracting first 5 PCs and each kennel-club grouping scheme
skulls <- cbind(SlicerMorph.repc[, 1:5], 
                "UKC" = factor(SlicerMorph.repc$UKC, ordered = T, levels = UKC_group_order), 
                "AKC" = factor(SlicerMorph.repc$AKC, ordered = T, levels = AKC_group_order),
                "bitework" = factor(SlicerMorph.repc$Bitework),
                "scentwork" = factor(SlicerMorph.repc$Nosework))
skulls <- na.omit(skulls)

# Create a paired and ordered GPA-grouping object
mixdrop<-gpa$coords[,,order(dimnames(gpa$coords)[[3]])]
mixdrop<-mixdrop[,,-96]

reforge<-geomorph.data.frame(shape = mixdrop,
                             UKC = na.omit(factor(SlicerMorph.repc$UKC, ordered = T)),
                             AKC = na.omit(factor(SlicerMorph.repc$AKC, ordered = T)),
                             bitework = na.omit(factor(SlicerMorph.repc$Bitework[-96])),
                             scentwork = na.omit(factor(SlicerMorph.repc$Nosework[-96])))

# Create a function that subsets the mean landmarks for each group and does a pairwise subtraction and squaring of those means
meanforge <- function(target, group) {
  #sub-setting the means and sending them to a new object
  new.coords<-coords.subset(target[["shape"]], group = target[[group]])
  output_means<-lapply(new.coords, mshape)
  #perform the subtraction and squaring of the pairwise combinations
  result<- combn(output_means, 2, function(x) (x[[1]]-x[[2]])^2, simplify = FALSE)
  #rename the pairs so they're readable
  names(result)<-combn(names(output_means), 2, function(n) paste(n[1], "-", n[2]), simplify = TRUE)
  return(result)
}

#now run the function for each grouping scheme. Each member of the list will be named based on which two groups are compared
meanshape.UKC<-meanforge(reforge,"UKC")
meanshape.AKC<-meanforge(reforge,"AKC")
meanshape.nose<-meanforge(reforge,"scentwork")
meanshape.bite<-meanforge(reforge,"bitework")

```

Reformatting data for visualization:

```{r}
calc_gpa_dist <- function(dat){
  require(tidyr)
  n <- length(names(dat))
  results <- matrix(NA, nrow = nrow(dat[[1]]), ncol = n)
  results <- as.data.frame(results)
  results <- cbind(seq(1,nrow(results)), results)
  colnames(results) <- c("landmark",names(dat))
  
  for(i in names(dat)){
    results[[i]] <- sqrt(dat[[i]][,"X"]^2 + dat[[i]][,"Y"]^2 + dat[[i]][,"Z"]^2)
  }
  results_long <- pivot_longer(results, cols = -"landmark", names_to = "comparison")
  results_long$landmark <- factor(results_long$landmark)
  return(results_long)
}

meanshape.AKC[["plotting"]] <- calc_gpa_dist(meanshape.AKC)
meanshape.UKC[["plotting"]] <- calc_gpa_dist(meanshape.UKC)
meanshape.bite[["plotting"]] <- calc_gpa_dist(meanshape.bite)
meanshape.bite[["cutoff"]] <- data.frame("mean" = mean(meanshape.bite[["plotting"]]$value), 
                                        "sd" = sd(meanshape.bite[["plotting"]]$value))
meanshape.nose[["plotting"]] <- calc_gpa_dist(meanshape.nose)
meanshape.nose[["cutoff"]] <- data.frame("mean" = mean(meanshape.nose[["plotting"]]$value), 
                                        "sd" = sd(meanshape.nose[["plotting"]]$value))

meanshape.AKC[["plotting"]]$short <- ifelse(grepl("toy", meanshape.AKC[["plotting"]]$comparison, 
                                                  ignore.case = T),
                                           "toy", 
                                           ifelse(grepl("natural", meanshape.AKC[["plotting"]]$comparison,
                                                        ignore.case = T),
                                                  "natural", "other"))
meanshape.AKC[["plotting"]]$short <- factor(meanshape.AKC[["plotting"]]$short, 
                                            ordered = T, levels = c("toy", "natural", "other"))
meanshape.AKC[["cutoff"]] <- data.frame("mean" = mean(meanshape.AKC[["plotting"]]$value), 
                                        "sd" = sd(meanshape.AKC[["plotting"]]$value))
meanshape.UKC[["plotting"]]$short <- ifelse(grepl("companion", meanshape.UKC[["plotting"]]$comparison,
                                                      ignore.case = T),
                                           "companion", 
                                           ifelse(grepl("natural", meanshape.UKC[["plotting"]]$comparison,
                                                      ignore.case = T),
                                           "natural", "other"))
meanshape.UKC[["plotting"]]$short <- factor(meanshape.UKC[["plotting"]]$short, 
                                            ordered = T, levels = c("companion", "natural", "other"))
meanshape.UKC[["cutoff"]] <- data.frame("mean" = mean(meanshape.UKC[["plotting"]]$value), 
                                        "sd" = sd(meanshape.UKC[["plotting"]]$value))

```

AKC & UKC groups:
```{r}
p_UKC_compare <- ggplot(meanshape.UKC[["plotting"]], aes(landmark, value, color = short)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.UKC[["cutoff"]]$mean+2*meanshape.UKC[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Comparison against") +
  ylab("DFA distance squared") +
  ggtitle("UKC group comparisons") +
  theme_bw() + 
  theme(legend.position = "inside", legend.position.inside = c(0.75,0.65),
        legend.background = element_rect(color = "gray30", fill = "white", linetype="solid",
                                         linewidth = 0.2))

p_AKC_compare <- ggplot(meanshape.AKC[["plotting"]], aes(landmark, value, color = short)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.AKC[["cutoff"]]$mean+2*meanshape.AKC[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Comparison against") +
  ylab("DFA distance squared") +
  ggtitle("AKC group comparisons") +
  theme_bw() +
    theme(legend.position = "inside", legend.position.inside = c(0.75,0.65),
        legend.background = element_rect(color = "gray30", fill = "white", linetype="solid",
                                         linewidth = 0.2))
p_AKC_compare / p_UKC_compare
```
Nosework and Bitework: 

```{r}
p_bite_compare <-  ggplot(meanshape.bite[["plotting"]], aes(landmark, value, color = comparison)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.bite[["cutoff"]]$mean+2*meanshape.bite[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Group-group\ncomparison") +
  ylab("DFA distance squared") +
  ggtitle("Bite-work group comparisons") +
  theme_bw()
p_nose_compare <- ggplot(meanshape.nose[["plotting"]], aes(landmark, value, color = comparison)) + 
  geom_point(position = position_jitter(width = 0.1)) + 
  geom_hline(yintercept = meanshape.nose[["cutoff"]]$mean+2*meanshape.nose[["cutoff"]]$sd,
             lty = 2) +
  scale_color_viridis_d(name = "Group-group\ncomparison") +
  ylab("DFA distance squared") +
  ggtitle("Scent-work group comparisons") +
  theme_bw()

p_bite_compare / p_nose_compare + plot_layout(guides = "collect")
```

## MANOVA 

```{r}
man_UKC <- manova(as.matrix(skulls[,1:5])~skulls$UKC)
summary.aov(man_UKC, test="Pillai")
```

```{r}
lda_UKC <- MASS::lda(skulls$UKC~as.matrix(skulls[,1:5]))
lda_UKC
```

## Testing of Functional Groups

```{r fxn-groupings, echo=FALSE, message=FALSE, warning=FALSE, fig.height=3.5, fig.cap="Bitework and scent work."}
fxn_group_palette <- munch_palette("Murderer",8)[c(1:3,5)]
pbite <- ggplot(SlicerMorph.repc, aes(PC.1, PC.2, color = Bitework, 
                                   fill = Bitework,
                                   shape = Bitework)) + 
  geom_point() +
  stat_ellipse(geom = "polygon", level = 0.95, alpha = 0.1) +
  scale_shape_manual(values = c(21, 23, 0, 2), name = " ") +
  scale_color_manual(values = fxn_group_palette, name = " ") + 
  scale_fill_manual(values = fxn_group_palette, name = " ") +
  xlab("PC 1 (Var = 50.2%)") + 
  ylab(" ") +
  ggtitle("Selected for bite work") +
  theme_bw()
pscent <- ggplot(SlicerMorph.repc, aes(PC.1, PC.2, color = Nosework, 
                                   fill = Nosework,
                                   shape = Nosework)) + 
  geom_point() +
  stat_ellipse(geom = "polygon", level = 0.95, alpha = 0.1) +
  scale_shape_manual(values = c(21, 23, 0, 2), name = " ") +
  scale_color_manual(values = fxn_group_palette, name = " ") + 
  scale_fill_manual(values = fxn_group_palette, name = " ") +
  xlab("PC 1 (Var = 50.2%)") + 
  ylab("PC 2 (Var = 13.3%)") +
  ggtitle("Selected for scent work") +
  theme_bw()
pscent + pbite + plot_layout(guides = "collect")

```

```{r bite-force, echo=FALSE, message=FALSE, warning=FALSE}
bite_data <- data.frame("Breed" = SlicerMorph.repc$Breed, 
                        "Bitework" = SlicerMorph.repc$Bitework, 
                        "Domestic" = SlicerMorph.repc$domestic, 
                        "UKC" = SlicerMorph.repc$UKC, 
                        "AKC" = SlicerMorph.repc$AKC,
                        "canine" = SlicerMorph.repc$bfq_canine, 
                        "carnassial" = SlicerMorph.repc$bfq_carnassial)
bite_data_long <- pivot_longer(bite_data, cols = c("canine","carnassial"))
pforce <- ggplot(bite_data_long, aes(Bitework, value, fill = name)) + 
  geom_boxplot(alpha = 0.6, outlier.shape = NA) + 
  geom_point(alpha = 0.5, position = position_jitterdodge(jitter.width = 0.2), shape = 21) +
  scale_fill_manual(values = munch_palette("YellowLog",2), name = " ") +
  ylab("Bite-force quotient") + xlab("Selected for bite work") +
  theme_bw()
pforce
```

```{r bite-force-stats}
bite_yes_canine <- bite_data$canine[bite_data$Bitework == "yes"]
bite_no_canine <- bite_data$canine[bite_data$Bitework == "no"]
shapiro.test(bite_yes_canine)
shapiro.test(bite_no_canine)
t.test(bite_yes_canine, bite_no_canine)

bite_yes_carnassial <- bite_data$carnassial[bite_data$Bitework == "yes"]
bite_no_carnassial <- bite_data$carnassial[bite_data$Bitework == "no"]
shapiro.test(bite_yes_carnassial)
shapiro.test(bite_no_carnassial)
t.test(bite_yes_carnassial, bite_no_carnassial)

bite_natural_canine <- bite_data$canine[bite_data$Bitework == "NATURAL"]
shapiro.test(bite_natural_canine)
bite_fox_canine <- bite_data$canine[bite_data$Bitework == "FOX"]
shapiro.test(bite_fox_canine)

t.test(bite_yes_canine, bite_natural_canine)
t.test(bite_yes_canine, bite_fox_canine)
```

## For the paper: 

Figure 2: 

```{r fig-2, echo=FALSE, warning=FALSE, fig.cap="A. K-means clustering plot. B. AKC groupings. C. UKC groupings.", fig.height=12, fig.width=10}
design <- 
  "AAAAAAAA#
   BBBBCCCC#
   DDDDDDDDD"
pkmean + pAKC + pUKC +
  (p_AKC_compare + p_UKC_compare) + 
  plot_layout(design = design) +
  plot_annotation(tag_levels = "A")
ggsave("./results/figures/figure2.pdf", height = 12, width = 10)
```

```{r fig-3, echo=FALSE, warning=FALSE, fig.cap="A. K-means clustering plot. B. AKC groupings. C. UKC groupings.", fig.height=7.5, fig.width=12}
# (p_CVA_AKC + p_CVA_UKC) + 
#  plot_annotation(tag_levels = "A") + 
#  plot_layout(guides = "collect") & theme(legend.position = "bottom")
#ggsave("./results/figures/figure3.pdf")
```

Figure 4: 

```{r fig-4, echo=FALSE, warning=FALSE, fig.cap="K-means clustering plot.", fig.height=7.5, fig.width=10}
(pscent + pbite + plot_layout(guides = "collect")) / pforce  + plot_annotation(tag_levels = "A")
ggsave("./results/figures/figure4.pdf")
```




